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Thermal conductivity of hydrogenated amorphous silicon
PERGAMON
Solid State Communications 120 (2001) 525±530
www.elsevier.com/locate/ssc
Thermal conductivity of hydrogenated amorphous silicon N. Attaf, M.S. Aida*, L. Hadjeris Laboratoire de Physique des Couches Minces et Interfaces, Unite de Recherche de Physique des MateÂriaux et Applications, Universite de Constantine 25000, Constantine, Algeria Received 30 January 2001; received in revised form 8 August 2001; accepted 1 October 2001 by P. Burlet
Abstract The thermal conductivity of amorphous silicon thin ®lms is measured in one dimension steady state condition. The experimental method is based on heating the sample front surface and monitoring the temperatures at its two sides. The experiments were carried out in conditions ensuring one-direction heat ¯ow from top to bottom throughout the sample thickness. Sputtered a-Si:H ®lms prepared with different conditions are used in order to investigate the dependence of thermal conductivity on material properties (i.e. hydrogen content and microstructure). The results show that, ®rstly, amorphous silicon is a very bad thermal conductor material. Secondly, the disorder in the ®lm network plays an important role in thermal conduction. The highly disordered ®lm exhibits the lowest thermal conductivity. q 2001 Elsevier Science Ltd. All rights reserved. PACS: 61.43; 65.50; 81.15 Keywords: A. Amorphous semiconductors; A. Thin ®lms; D. Thermal conductivity
1. Introduction Amorphous hydrogenated silicon (a-Si:H) is an interesting material for a basic technical and theoretical understanding of amorphous semiconductors physics. It is used especially in solar cells and thin ®lm transistor fabrication. Thus for these applications, properties related to the carriers density, transport, generation and recombination such as dark conductivity, photoconductivity, density of gap states, mobility, lifetime etc. are important to be known. Hence, a worldwide effort has gone into characterization of these parameters and optimization of the preparation conditions. Therefore, structural electrical and optical properties of amorphous silicon were extensively studied. Despite this extensive effort of material characterization, thermal conductivity of hydrogenated amorphous silicon remains unknown. The determination of thermal conductivity is helpful to study amorphous silicon crystallization, computation, and control of the temperature pro®le and heat propagation especially during thermal annealing or laser crystallization [1±5]. Thermal conductivity may also play a key role during ®lm growth. Film surface is heated by * Corresponding author. Tel.: 1213-31-61-47-11; fax: 1213-3162-34-89.
plasma energetic species impinging, in the case of ®lms with low thermal conduction, the heat could not be easily dissipated, and consequently ®lm microstructure is altered [6,7]. Many techniques have been proposed to measure the thermal conduction of thin ®lms, namely a.c. calorimetric method [8], pulse transient hot strip technique [9], heat pulse technique [10], and transient thermo-re¯ectance method [11]. However all these techniques need special equipments and are suitable only for metallic ®lms thicker than 1 mm. The aim of the present paper is the measurement of thermal conductivity of sputtered amorphous silicon. The used method is simple; it is based on temperature measurement at the two sides of the sample. Films prepared with different conditions were used in order to investigate the in¯uence of hydrogen content and disorder on their thermal conductivity. 2. Experimental details Samples used in the present study are prepared by RF sputtering of monocrystalline silicon target in an argon± hydrogen mixture atmosphere. The total gas pressure and hydrogen partial pressure are, respectively, 10 21 and 10 22 mb. The glass substrate temperature is kept constant
0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0038- 109 8( 01) 00428-8
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N. Attaf et al. / Solid State Communications 120 (2001) 525±530
Table 1 Films preparation conditions and characterization results. CH is the hydrogen content, Eoo is the Urbach tail, Ea.elec and Ea.th are, respectively, the electrical and thermal activation energies. teq is the required time to reach equilibrium Sample
Thickness ef (mm)
PRF (W)
CH (%)
Eoo (meV)
Ea.elec (eV)
Ea.th (eV)
teq (min)
a b c d
0.225 0.448 0.280 0.360
30 90 100 200
36 28 30 16
300 150 90 60
0.50 0.62 0.65 0.70
0.13 0.16 0.35 0.49
42 35 30 30
at 2008C. RF power is varied in the range of 30±200 W in order to modify disorder and hydrogen content in the ®lm network. The hydrogen content in ®lms network is determined from Infrared absorption. Films thickness and disorder have been deduced from the optical absorption in the UV±Visible region. These characteristics are listed in Table 1. Fig. 1 presents the scheme of the experimental set-up. Thermal conductivity determination is based on the measurement of temperatures at ®lm top surface and rear surface of the substrate. Temperatures variations with time are monitored until reaching steady-state condition. A thin tungsten ®lament with known electrical resistance R (10 V), heated by an electric current is used as heat source and placed in front of a-Si:H top surface. The substrate is placed on a copper disk, which is cooled with an external circuit of cold water with a regulated temperature ®xed at 88C. In this con®guration, the heat ¯ows from the heated a-Si:H top surface (T1) towards the cooled substrate bottom surface (T3), the temperature gradient being controllable. Stick-on thermocouples (NiCr/Ni) intended for surface temperature measurement, connected to multipoint data recorder are used for surface temperature (T1 and T3) measurements with an accuracy of 1.5%. The measurements are carried in vacuum in order to minimize heat transfer by convection. The heat ¯ux is estimated from the intensity measurement of electric current passing through the tungsten ®lament. The
heating temperature does not exceed the deposition temperature in order to avoid ®lm network microstructure modi®cation. At steady state conduction and by neglecting the heat losses at sample edges and the re¯ection at interfaces, the same heat ¯ux F is carried through the ®lm and the substrate, one can then write from Fourier law
F Kf
T1 2 T2 T 2 T3 Ks 2 ef es
1
T1, T2 and T3 are, respectively, the equilibrium temperatures reached at the top surface of ®lm, ®lm-substrate interface and the substrate bottom surface as labeled by 1, 2 and 3 in Fig. 1. Kf is the average thermal conductivity of amorphous silicon ®lm and Ks is the thermal conductivity of glass substrate. ef and es are the ®lm and substrate thickness, respectively. Since it is dif®cult to determine accurately the temperature T2 at the ®lm±substrate interface, the ®lm thermal conductivity Kf can also be estimated using only the measured temperatures T1 and T3. By analogy with electrical conductivity one can write
F
T 1 2 T2 T 2 T3 T 2 T3 2 1 lf ls leq
2
where l f and l s are the thermal resistance of ®lm and substrate, respectively. The equivalent resistance of ®lm and substrate l eq can be then written e e leq lf 1 ls f 1 s 3 Kf Ks The heat ¯ux F is also given by
F
Fig. 1. Schematic drawn of the experimental set-up.
RI 2 2S
4
R, I and S are tungsten ®lament resistance, heating current and ®lm surface, respectively. Here we must only consider the half of the total heat RI 2 of tungsten ®lament, i.e. only radiation emitted from the surface towards the bottom half space is taken into account and re¯ection on the walls is neglected since they are cooled. Knowing heat ¯ux, temperature T1 and T3, the equivalent thermal resistance l eq can be calculated by using Eq. (2) and then the thermal conductivity Kf of a-Si:H ®lm and T2 can be deduced. Heating ¯ux and ®lm temperature can be controlled by varying the current intensity in the range of 0.5±2 A,
N. Attaf et al. / Solid State Communications 120 (2001) 525±530
Fig. 2. Time pro®le of temperature variation obtained at the two sides of different samples prepared with various RF powers (a: 30 W, b: 90 W, c: 100 W and d: 200 W).
thereafter the variation of thermal conductivity with average ®lm temperature can be deduced.
3. Results and discussion Fig. 2 shows a typical pro®le of temperatures (T1 and T3) variation with time at the two sides of samples prepared with various RF powers. T1 is the measured temperature at the top side of ®lms. As can be seen, the temperature T3 at the bottom remains constant for all cases. This is due to the temperature regulation at the sample holder. Nevertheless,
527
the temperature at the top of ®lm rises with time and saturates after a certain time. In this case, a constant temperature gradient is present between the sample edges. Then, a steady state heat ¯ux is established from the top to bottom through the sample. As reported in Table 1, the main saturation time observed in the whole samples used in this study is in the order of 13 min. The longest time required for steady state establishment is met in the case (a) of rich hydrogen content and disordered ®lm, though it is a thinner one. This suggests, as we shall see later, that rich hydrogen and disordered ®lm exhibit low thermal conductivity. It is well known that RF power controls the properties of a-Si:H ®lms such as hydrogen content and microstructure. In table I we have reported some characteristics of used samples in the present study especially hydrogen content and disorder. As can be deduced, when the deposition RF power is increased, the hydrogen content and the disorder in the ®lm network are reduced, i.e. ®lms deposited with low RF powers are hydrogen rich on one hand, and highly disordered on the other hand [12]. Moreover, it is well known that in RF sputtered material hydrogen is bonded mainly in polyhydride con®gurations (SiH3, SiH2 or (SiH2)n) [13], contrarily to ®lms deposited by glow discharge method where mainly monohydride bonds are present. Thus, sputtered material is more porous than glow discharged material and the porosity size increases with hydrogen content. This is consistent with the correlation between hydrogen content and thermal conductivity variations as a function of deposition RF power, as shown in Fig. 3. Thermal energy may be transported in solids by two modes: phonons propagation through lattice vibration and
Fig. 3. Variation of thermal conductivity and hydrogen content of amorphous silicon thin ®lms with RF power ®lm deposition.
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N. Attaf et al. / Solid State Communications 120 (2001) 525±530
Fig. 4. Variation of thermal conductivity and valence band tail width as a function of RF power.
free electrons displacement. The contribution of the latter mode is generally low in amorphous semiconductors, since the presence of a large density of gap states reduces the mobility and the lifetime of free electrons leading to a weaker electrical conductivity than in crystalline material. On the other hand, the presence of dangling bonds reduces thermal conduction. Amorphous silicon thin ®lms usually show a large density de®cit or void fraction, which can have Ê [4]. These micro-porosities cause disa diameter of 20 A continuities in the ®lm network and then hinder phonon propagation. Therefore, a-Si:H ®lms thermal conductivity is low than in the well organized monocrystalline silicon material, where the thermal conductivity is in the order of 1500 mW cm 21 K 21. The highest measured value of thermal conductivity in our samples is in the order of 0.6 mW cm 21 K 21 at room temperature and 5.5 mW cm 21 K 21 at 373 K. For pure a-Si, Goldsmid et al. [14] found at room temperature a value of 26 mW cm 21 K 21. In a modeling study, Webber et al. [15] emphasized amorphous silicon thermal conductivity variation with temperature in the range of 100±1400 K, they reported the value of 7 mW cm 21 K 21 at 300 K and 10 mW cm 21 K 21 for T . 400 K: Our results are relatively low by comparison to the published ones, this is due to the deposition method. As mentioned in Section 2, our ®lms are elaborated by sputtering technique. It is well recognized that this method, which is physical vapor deposition (PVD)-like, led to the columnar growth, then material prepared by this method exhibit microheterogeneity, large defect density and high disorder than material prepared by chemical vapor deposition (CVD)-like condition namely glow discharge technique [16,17]. Hence, disorder and defect density present in sputtered amorphous silicon are the responsible for the reduction of material thermal conductivity. For further insight on the role of disorder we have reported in
Fig. 4, as a function of deposition RF power, in the same plot the variation of thermal conductivity and the valance band tail width which is used as disorder probe in the ®lm network. During their growth, ®lms elaborated with high RF power are under intensive argon ions bombardment [18]. The carried energy by these ions, on the growing surface, favors the network restructuration and material densi®cation. Therefore, as can be seen, the enhancement in material thermal conductivity with an increasing deposition RF power is due to the decrease in material disorder. The ratio of thermal conductivity in amorphous silicon to thermal conductivity in monocrystalline silicon is in the order of 10 24 ±10 22, while the ratio of their electrical conductivity is in the range of 10 210 ±10 25. The difference between the two ratios suggests that the thermal conductivity in amorphous silicon is achieved mainly by phonon propagation. Therefore, one expects that micro-porosities concentration and their size control the thermal conductivity. This is consistent with the results of Figs. 3 and 4, since ®lms deposited with low powers, i.e. highly porous and disordered, exhibit low thermal conductivities. It is established that the frequency of different vibrational modes of Si±H bond (stretching, wagging and rocking) are localized in infrared region [13,19]. A part of heat is then absorbed by the vibration of the different Si±H bonds present in the material network. Consequently, the increase of hydrogen content in a-Si:H ®lms reduces the heat conduction as reported in Fig. 3 the thermal conductivity is lower for the richest hydrogen ®lms. Ivanda et al. [5] investigate the laser crystallization of magnetron sputtered amorphous silicon ®lms with different thickness and hydrogen concentrations. They inferred that laser crystallization is a thermally induced process and concluded that the laser threshold power for transition
N. Attaf et al. / Solid State Communications 120 (2001) 525±530
529
Fig. 5. In¯uence of the mean temperature of the ®lm on the thermal conductivity for samples prepared with different RF powers.
from the amorphous to crystalline states depends among themselves, on the hydrogen content in the ®lms. They observed a decrease in the power threshold with the increase of hydrogen content. During laser annealing, the carried heat cannot be easily evacuated in low thermal conducting ®lm, thereafter surface ®lm temperature rises quickly and then the crystallization power is reduced. Hence, their results can be explained in terms of thermal conductivity
reduction in rich hydrogen ®lms, which is consistent with our results. Fig. 5 displays the variation of thermal conductivity of different a-Si:H ®lms as a function of mean temperature of the ®lm, taken equal to 1=2 T1 1 T2 : As can be seen, the thermal conductivity increases linearly with the temperature. This is consistent with the reported general behavior of thermal conductivity in amorphous material [20].
Fig. 6. Electrical and thermal activation energies of amorphous silicon thin ®lms versus deposition RF power.
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N. Attaf et al. / Solid State Communications 120 (2001) 525±530
Thermal conductivity is expressed with kinetic terms as [21] K
Cth nl 3
where Cth, n and l are, respectively, the material thermal capacity, phonon velocity and phonon mean free path. In amorphous material, defects such as disorder and dangling bonds give rise to a large amount of phonon scattering, which is associated to a thermal resistance. This scattering mechanism limits phonon free mean path in amorphous silicon. The observed increase with temperature in the thermal conductivity of amorphous silicon can be then explained by the increase in the thermal capacity. As can be deduced from Fig. 5, heat conductivity in different ®lms is thermally activated. The activation energies are calculated from the slope of the curves ln K f 1=T: As shown in Fig. 6, the activation energy presents the same variation trend as electrical conduction with increasing preparation RF power. Films deposited with low RF powers are less thermally activated than ®lms prepared with high powers. As can be seen, the difference between electrical and thermal activation energies is the smallest in the case of ®lms deposited at high RF power. This suggests that the contribution of electron displacement mode in heat conduction may become signi®cant in the case of ®lms prepared with high RF power, i.e. less porous. The thermal conductivity of amorphous silicon thin ®lm may play an important role during ®lm growth. It is worth noting that during growth ®lm surface is under an intensive bombardment by different species coming from the plasma especially electrons and argon energetic ions. Argon ions striking the surface are not incorporated in the ®lm network, but they dissipate their kinetic energy. This surface impingement causes the surface heating. On the other hand, since the thermal conductivity of amorphous silicon is low as reported in this paper, the carried heat on the ®lm-growing surface is not easily evacuated towards the substrate. Hence, the surface temperature rises and can reach, at a critical thickness, the crystallization temperature of the material. Therefore, amorphous silicon microstructure is thickness dependent. This could explain the observed microstructure irregularity with thickness in sputtered amorphous silicon [6,7]. 4. Conclusion In the present study we have measured the thermal conductivity of sputtered amorphous silicon thin ®lms. The in¯uence of hydrogen concentration and disorder in the ®lm network are investigated. For this purpose ®lms prepared with different RF powers are used. The main
results obtained suggest that amorphous silicon thin ®lms exhibit a low thermal conduction. This is due mainly to the presence of microporosities in the ®lm network. The thermal conductivity is lowered in rich hydrogen and highly disordered ®lms. This is explained in terms of phonon scattering due to increases in the porosity size. The conduction is ensured mainly by the phonon propagation. However, the contribution of electrons motion appears with increasing preparation RF power. Acknowledgements We would like to thank K. Belkacem Bouricha for her valuable help with the manuscript redaction. References [1] K. Zellama, P. Germain, S. Squelard, J.C. Bourgoin, P.A. Thomas, J. Appl. Phys. 50 (1979) 6995. [2] S.A. Kokorowski, G.L. Olson, J.A. Roth, L.D. Hess, Phys. Rev. Lett. 48 (1982) 498. [3] P.S. Peerely, J.Y. Tsao, S.R. Stif¯er, M.O. Thompson, Appl. Phys. Lett. 52 (1988) 203. [4] S. Logothedis, G. Kiriokidis, E.C. Paloura, J. Appl. Phys. 70 (1991) 2791. [5] M. Ivanda, K. Furic, M. Persin, D. Gracin, J. Appl. Phys. 70 (1991) 4637. [6] R.C. Ross, R. Messier, J. Appl. Phys. 52 (1981) 5328. [7] M.S. Aida, K. Mirouh, Phys. Status Solidi A 136 (1993) K31. [8] I. Hatta, Y. Suga, R. Kato, A. Maesono, Rev. Sci. Instrum. 56 (1985) 1643. [9] S.E. Gustafsson, M.A. Chohan, K. Ahmed, A. Maqsood, J. Appl. Phys. 55 (1984) 3348. [10] W.M. Goubau, R.A. Tait, Phys. Rev. Lett. 34 (1975) 1220. [11] C.A. Paddock, G.L. Eesley, J. Appl. Phys. 60 (1986) 285. [12] S. Rahman, Magister Thesis Universite de Constantine, 1995. [13] D.A. Anderson, W. Paul, Philos. Mag. B44 (1981) 5329. [14] H.J. Goldsmid, M.M. Kaila, G.L. Paul, Phys. Status Solidi A 76 (1) (1983) K31±K33. [15] H.C. Webber, A.G. Cullis, N.G. Chew, Appl. Phys. Lett. (USA) 43 (7) (1983) 669±671. [16] C.C. Tsai, J.C. Knights, G. Chang, B. Wacker, J. Appl. Phys. 59 (1986) 2998. [17] D. Jousse, E. Bustarret, F. Boulitrop, Solid State Commun. 55 (1985) 435. [18] M.S. Aida, J. Non Cryst. Solids 160 (1993) 99. [19] M.H. Brodsky, M. Cardona, J.J. Cuomo, Phys. Rev. B16 (1977) 3556. [20] J. Berman, Thermal Conduction in Solids, Oxford Sciences Publication 1976 p. 104. [21] H.M. Rosenberg, The Solid State, 3rd ed, Oxford Sciences Publication 1988 p. 96.
Solid State Communications 120 (2001) 525±530
www.elsevier.com/locate/ssc
Thermal conductivity of hydrogenated amorphous silicon N. Attaf, M.S. Aida*, L. Hadjeris Laboratoire de Physique des Couches Minces et Interfaces, Unite de Recherche de Physique des MateÂriaux et Applications, Universite de Constantine 25000, Constantine, Algeria Received 30 January 2001; received in revised form 8 August 2001; accepted 1 October 2001 by P. Burlet
Abstract The thermal conductivity of amorphous silicon thin ®lms is measured in one dimension steady state condition. The experimental method is based on heating the sample front surface and monitoring the temperatures at its two sides. The experiments were carried out in conditions ensuring one-direction heat ¯ow from top to bottom throughout the sample thickness. Sputtered a-Si:H ®lms prepared with different conditions are used in order to investigate the dependence of thermal conductivity on material properties (i.e. hydrogen content and microstructure). The results show that, ®rstly, amorphous silicon is a very bad thermal conductor material. Secondly, the disorder in the ®lm network plays an important role in thermal conduction. The highly disordered ®lm exhibits the lowest thermal conductivity. q 2001 Elsevier Science Ltd. All rights reserved. PACS: 61.43; 65.50; 81.15 Keywords: A. Amorphous semiconductors; A. Thin ®lms; D. Thermal conductivity
1. Introduction Amorphous hydrogenated silicon (a-Si:H) is an interesting material for a basic technical and theoretical understanding of amorphous semiconductors physics. It is used especially in solar cells and thin ®lm transistor fabrication. Thus for these applications, properties related to the carriers density, transport, generation and recombination such as dark conductivity, photoconductivity, density of gap states, mobility, lifetime etc. are important to be known. Hence, a worldwide effort has gone into characterization of these parameters and optimization of the preparation conditions. Therefore, structural electrical and optical properties of amorphous silicon were extensively studied. Despite this extensive effort of material characterization, thermal conductivity of hydrogenated amorphous silicon remains unknown. The determination of thermal conductivity is helpful to study amorphous silicon crystallization, computation, and control of the temperature pro®le and heat propagation especially during thermal annealing or laser crystallization [1±5]. Thermal conductivity may also play a key role during ®lm growth. Film surface is heated by * Corresponding author. Tel.: 1213-31-61-47-11; fax: 1213-3162-34-89.
plasma energetic species impinging, in the case of ®lms with low thermal conduction, the heat could not be easily dissipated, and consequently ®lm microstructure is altered [6,7]. Many techniques have been proposed to measure the thermal conduction of thin ®lms, namely a.c. calorimetric method [8], pulse transient hot strip technique [9], heat pulse technique [10], and transient thermo-re¯ectance method [11]. However all these techniques need special equipments and are suitable only for metallic ®lms thicker than 1 mm. The aim of the present paper is the measurement of thermal conductivity of sputtered amorphous silicon. The used method is simple; it is based on temperature measurement at the two sides of the sample. Films prepared with different conditions were used in order to investigate the in¯uence of hydrogen content and disorder on their thermal conductivity. 2. Experimental details Samples used in the present study are prepared by RF sputtering of monocrystalline silicon target in an argon± hydrogen mixture atmosphere. The total gas pressure and hydrogen partial pressure are, respectively, 10 21 and 10 22 mb. The glass substrate temperature is kept constant
0038-1098/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0038- 109 8( 01) 00428-8
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N. Attaf et al. / Solid State Communications 120 (2001) 525±530
Table 1 Films preparation conditions and characterization results. CH is the hydrogen content, Eoo is the Urbach tail, Ea.elec and Ea.th are, respectively, the electrical and thermal activation energies. teq is the required time to reach equilibrium Sample
Thickness ef (mm)
PRF (W)
CH (%)
Eoo (meV)
Ea.elec (eV)
Ea.th (eV)
teq (min)
a b c d
0.225 0.448 0.280 0.360
30 90 100 200
36 28 30 16
300 150 90 60
0.50 0.62 0.65 0.70
0.13 0.16 0.35 0.49
42 35 30 30
at 2008C. RF power is varied in the range of 30±200 W in order to modify disorder and hydrogen content in the ®lm network. The hydrogen content in ®lms network is determined from Infrared absorption. Films thickness and disorder have been deduced from the optical absorption in the UV±Visible region. These characteristics are listed in Table 1. Fig. 1 presents the scheme of the experimental set-up. Thermal conductivity determination is based on the measurement of temperatures at ®lm top surface and rear surface of the substrate. Temperatures variations with time are monitored until reaching steady-state condition. A thin tungsten ®lament with known electrical resistance R (10 V), heated by an electric current is used as heat source and placed in front of a-Si:H top surface. The substrate is placed on a copper disk, which is cooled with an external circuit of cold water with a regulated temperature ®xed at 88C. In this con®guration, the heat ¯ows from the heated a-Si:H top surface (T1) towards the cooled substrate bottom surface (T3), the temperature gradient being controllable. Stick-on thermocouples (NiCr/Ni) intended for surface temperature measurement, connected to multipoint data recorder are used for surface temperature (T1 and T3) measurements with an accuracy of 1.5%. The measurements are carried in vacuum in order to minimize heat transfer by convection. The heat ¯ux is estimated from the intensity measurement of electric current passing through the tungsten ®lament. The
heating temperature does not exceed the deposition temperature in order to avoid ®lm network microstructure modi®cation. At steady state conduction and by neglecting the heat losses at sample edges and the re¯ection at interfaces, the same heat ¯ux F is carried through the ®lm and the substrate, one can then write from Fourier law
F Kf
T1 2 T2 T 2 T3 Ks 2 ef es
1
T1, T2 and T3 are, respectively, the equilibrium temperatures reached at the top surface of ®lm, ®lm-substrate interface and the substrate bottom surface as labeled by 1, 2 and 3 in Fig. 1. Kf is the average thermal conductivity of amorphous silicon ®lm and Ks is the thermal conductivity of glass substrate. ef and es are the ®lm and substrate thickness, respectively. Since it is dif®cult to determine accurately the temperature T2 at the ®lm±substrate interface, the ®lm thermal conductivity Kf can also be estimated using only the measured temperatures T1 and T3. By analogy with electrical conductivity one can write
F
T 1 2 T2 T 2 T3 T 2 T3 2 1 lf ls leq
2
where l f and l s are the thermal resistance of ®lm and substrate, respectively. The equivalent resistance of ®lm and substrate l eq can be then written e e leq lf 1 ls f 1 s 3 Kf Ks The heat ¯ux F is also given by
F
Fig. 1. Schematic drawn of the experimental set-up.
RI 2 2S
4
R, I and S are tungsten ®lament resistance, heating current and ®lm surface, respectively. Here we must only consider the half of the total heat RI 2 of tungsten ®lament, i.e. only radiation emitted from the surface towards the bottom half space is taken into account and re¯ection on the walls is neglected since they are cooled. Knowing heat ¯ux, temperature T1 and T3, the equivalent thermal resistance l eq can be calculated by using Eq. (2) and then the thermal conductivity Kf of a-Si:H ®lm and T2 can be deduced. Heating ¯ux and ®lm temperature can be controlled by varying the current intensity in the range of 0.5±2 A,
N. Attaf et al. / Solid State Communications 120 (2001) 525±530
Fig. 2. Time pro®le of temperature variation obtained at the two sides of different samples prepared with various RF powers (a: 30 W, b: 90 W, c: 100 W and d: 200 W).
thereafter the variation of thermal conductivity with average ®lm temperature can be deduced.
3. Results and discussion Fig. 2 shows a typical pro®le of temperatures (T1 and T3) variation with time at the two sides of samples prepared with various RF powers. T1 is the measured temperature at the top side of ®lms. As can be seen, the temperature T3 at the bottom remains constant for all cases. This is due to the temperature regulation at the sample holder. Nevertheless,
527
the temperature at the top of ®lm rises with time and saturates after a certain time. In this case, a constant temperature gradient is present between the sample edges. Then, a steady state heat ¯ux is established from the top to bottom through the sample. As reported in Table 1, the main saturation time observed in the whole samples used in this study is in the order of 13 min. The longest time required for steady state establishment is met in the case (a) of rich hydrogen content and disordered ®lm, though it is a thinner one. This suggests, as we shall see later, that rich hydrogen and disordered ®lm exhibit low thermal conductivity. It is well known that RF power controls the properties of a-Si:H ®lms such as hydrogen content and microstructure. In table I we have reported some characteristics of used samples in the present study especially hydrogen content and disorder. As can be deduced, when the deposition RF power is increased, the hydrogen content and the disorder in the ®lm network are reduced, i.e. ®lms deposited with low RF powers are hydrogen rich on one hand, and highly disordered on the other hand [12]. Moreover, it is well known that in RF sputtered material hydrogen is bonded mainly in polyhydride con®gurations (SiH3, SiH2 or (SiH2)n) [13], contrarily to ®lms deposited by glow discharge method where mainly monohydride bonds are present. Thus, sputtered material is more porous than glow discharged material and the porosity size increases with hydrogen content. This is consistent with the correlation between hydrogen content and thermal conductivity variations as a function of deposition RF power, as shown in Fig. 3. Thermal energy may be transported in solids by two modes: phonons propagation through lattice vibration and
Fig. 3. Variation of thermal conductivity and hydrogen content of amorphous silicon thin ®lms with RF power ®lm deposition.
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N. Attaf et al. / Solid State Communications 120 (2001) 525±530
Fig. 4. Variation of thermal conductivity and valence band tail width as a function of RF power.
free electrons displacement. The contribution of the latter mode is generally low in amorphous semiconductors, since the presence of a large density of gap states reduces the mobility and the lifetime of free electrons leading to a weaker electrical conductivity than in crystalline material. On the other hand, the presence of dangling bonds reduces thermal conduction. Amorphous silicon thin ®lms usually show a large density de®cit or void fraction, which can have Ê [4]. These micro-porosities cause disa diameter of 20 A continuities in the ®lm network and then hinder phonon propagation. Therefore, a-Si:H ®lms thermal conductivity is low than in the well organized monocrystalline silicon material, where the thermal conductivity is in the order of 1500 mW cm 21 K 21. The highest measured value of thermal conductivity in our samples is in the order of 0.6 mW cm 21 K 21 at room temperature and 5.5 mW cm 21 K 21 at 373 K. For pure a-Si, Goldsmid et al. [14] found at room temperature a value of 26 mW cm 21 K 21. In a modeling study, Webber et al. [15] emphasized amorphous silicon thermal conductivity variation with temperature in the range of 100±1400 K, they reported the value of 7 mW cm 21 K 21 at 300 K and 10 mW cm 21 K 21 for T . 400 K: Our results are relatively low by comparison to the published ones, this is due to the deposition method. As mentioned in Section 2, our ®lms are elaborated by sputtering technique. It is well recognized that this method, which is physical vapor deposition (PVD)-like, led to the columnar growth, then material prepared by this method exhibit microheterogeneity, large defect density and high disorder than material prepared by chemical vapor deposition (CVD)-like condition namely glow discharge technique [16,17]. Hence, disorder and defect density present in sputtered amorphous silicon are the responsible for the reduction of material thermal conductivity. For further insight on the role of disorder we have reported in
Fig. 4, as a function of deposition RF power, in the same plot the variation of thermal conductivity and the valance band tail width which is used as disorder probe in the ®lm network. During their growth, ®lms elaborated with high RF power are under intensive argon ions bombardment [18]. The carried energy by these ions, on the growing surface, favors the network restructuration and material densi®cation. Therefore, as can be seen, the enhancement in material thermal conductivity with an increasing deposition RF power is due to the decrease in material disorder. The ratio of thermal conductivity in amorphous silicon to thermal conductivity in monocrystalline silicon is in the order of 10 24 ±10 22, while the ratio of their electrical conductivity is in the range of 10 210 ±10 25. The difference between the two ratios suggests that the thermal conductivity in amorphous silicon is achieved mainly by phonon propagation. Therefore, one expects that micro-porosities concentration and their size control the thermal conductivity. This is consistent with the results of Figs. 3 and 4, since ®lms deposited with low powers, i.e. highly porous and disordered, exhibit low thermal conductivities. It is established that the frequency of different vibrational modes of Si±H bond (stretching, wagging and rocking) are localized in infrared region [13,19]. A part of heat is then absorbed by the vibration of the different Si±H bonds present in the material network. Consequently, the increase of hydrogen content in a-Si:H ®lms reduces the heat conduction as reported in Fig. 3 the thermal conductivity is lower for the richest hydrogen ®lms. Ivanda et al. [5] investigate the laser crystallization of magnetron sputtered amorphous silicon ®lms with different thickness and hydrogen concentrations. They inferred that laser crystallization is a thermally induced process and concluded that the laser threshold power for transition
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Fig. 5. In¯uence of the mean temperature of the ®lm on the thermal conductivity for samples prepared with different RF powers.
from the amorphous to crystalline states depends among themselves, on the hydrogen content in the ®lms. They observed a decrease in the power threshold with the increase of hydrogen content. During laser annealing, the carried heat cannot be easily evacuated in low thermal conducting ®lm, thereafter surface ®lm temperature rises quickly and then the crystallization power is reduced. Hence, their results can be explained in terms of thermal conductivity
reduction in rich hydrogen ®lms, which is consistent with our results. Fig. 5 displays the variation of thermal conductivity of different a-Si:H ®lms as a function of mean temperature of the ®lm, taken equal to 1=2 T1 1 T2 : As can be seen, the thermal conductivity increases linearly with the temperature. This is consistent with the reported general behavior of thermal conductivity in amorphous material [20].
Fig. 6. Electrical and thermal activation energies of amorphous silicon thin ®lms versus deposition RF power.
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Thermal conductivity is expressed with kinetic terms as [21] K
Cth nl 3
where Cth, n and l are, respectively, the material thermal capacity, phonon velocity and phonon mean free path. In amorphous material, defects such as disorder and dangling bonds give rise to a large amount of phonon scattering, which is associated to a thermal resistance. This scattering mechanism limits phonon free mean path in amorphous silicon. The observed increase with temperature in the thermal conductivity of amorphous silicon can be then explained by the increase in the thermal capacity. As can be deduced from Fig. 5, heat conductivity in different ®lms is thermally activated. The activation energies are calculated from the slope of the curves ln K f 1=T: As shown in Fig. 6, the activation energy presents the same variation trend as electrical conduction with increasing preparation RF power. Films deposited with low RF powers are less thermally activated than ®lms prepared with high powers. As can be seen, the difference between electrical and thermal activation energies is the smallest in the case of ®lms deposited at high RF power. This suggests that the contribution of electron displacement mode in heat conduction may become signi®cant in the case of ®lms prepared with high RF power, i.e. less porous. The thermal conductivity of amorphous silicon thin ®lm may play an important role during ®lm growth. It is worth noting that during growth ®lm surface is under an intensive bombardment by different species coming from the plasma especially electrons and argon energetic ions. Argon ions striking the surface are not incorporated in the ®lm network, but they dissipate their kinetic energy. This surface impingement causes the surface heating. On the other hand, since the thermal conductivity of amorphous silicon is low as reported in this paper, the carried heat on the ®lm-growing surface is not easily evacuated towards the substrate. Hence, the surface temperature rises and can reach, at a critical thickness, the crystallization temperature of the material. Therefore, amorphous silicon microstructure is thickness dependent. This could explain the observed microstructure irregularity with thickness in sputtered amorphous silicon [6,7]. 4. Conclusion In the present study we have measured the thermal conductivity of sputtered amorphous silicon thin ®lms. The in¯uence of hydrogen concentration and disorder in the ®lm network are investigated. For this purpose ®lms prepared with different RF powers are used. The main
results obtained suggest that amorphous silicon thin ®lms exhibit a low thermal conduction. This is due mainly to the presence of microporosities in the ®lm network. The thermal conductivity is lowered in rich hydrogen and highly disordered ®lms. This is explained in terms of phonon scattering due to increases in the porosity size. The conduction is ensured mainly by the phonon propagation. However, the contribution of electrons motion appears with increasing preparation RF power. Acknowledgements We would like to thank K. Belkacem Bouricha for her valuable help with the manuscript redaction. References [1] K. Zellama, P. Germain, S. Squelard, J.C. Bourgoin, P.A. Thomas, J. Appl. Phys. 50 (1979) 6995. [2] S.A. Kokorowski, G.L. Olson, J.A. Roth, L.D. Hess, Phys. Rev. Lett. 48 (1982) 498. [3] P.S. Peerely, J.Y. Tsao, S.R. Stif¯er, M.O. Thompson, Appl. Phys. Lett. 52 (1988) 203. [4] S. Logothedis, G. Kiriokidis, E.C. Paloura, J. Appl. Phys. 70 (1991) 2791. [5] M. Ivanda, K. Furic, M. Persin, D. Gracin, J. Appl. Phys. 70 (1991) 4637. [6] R.C. Ross, R. Messier, J. Appl. Phys. 52 (1981) 5328. [7] M.S. Aida, K. Mirouh, Phys. Status Solidi A 136 (1993) K31. [8] I. Hatta, Y. Suga, R. Kato, A. Maesono, Rev. Sci. Instrum. 56 (1985) 1643. [9] S.E. Gustafsson, M.A. Chohan, K. Ahmed, A. Maqsood, J. Appl. Phys. 55 (1984) 3348. [10] W.M. Goubau, R.A. Tait, Phys. Rev. Lett. 34 (1975) 1220. [11] C.A. Paddock, G.L. Eesley, J. Appl. Phys. 60 (1986) 285. [12] S. Rahman, Magister Thesis Universite de Constantine, 1995. [13] D.A. Anderson, W. Paul, Philos. Mag. B44 (1981) 5329. [14] H.J. Goldsmid, M.M. Kaila, G.L. Paul, Phys. Status Solidi A 76 (1) (1983) K31±K33. [15] H.C. Webber, A.G. Cullis, N.G. Chew, Appl. Phys. Lett. (USA) 43 (7) (1983) 669±671. [16] C.C. Tsai, J.C. Knights, G. Chang, B. Wacker, J. Appl. Phys. 59 (1986) 2998. [17] D. Jousse, E. Bustarret, F. Boulitrop, Solid State Commun. 55 (1985) 435. [18] M.S. Aida, J. Non Cryst. Solids 160 (1993) 99. [19] M.H. Brodsky, M. Cardona, J.J. Cuomo, Phys. Rev. B16 (1977) 3556. [20] J. Berman, Thermal Conduction in Solids, Oxford Sciences Publication 1976 p. 104. [21] H.M. Rosenberg, The Solid State, 3rd ed, Oxford Sciences Publication 1988 p. 96.